Use mdbook-katex in pre-render mode for both books, pin mdBook to a compatible version, update build scripts and workflows, and replace the old MathJax regression tests with KaTeX coverage.
Replace manual mdBook installation in CI and Pages workflows with peaceiris/actions-mdbook@v2 and keep a regression test to ensure the action stays in use.
Move the English root site to mdBook, keep the Chinese site as a sub-book, and update CI/deploy to publish .mdbook outputs to docs/ and docs/cn/. Also add regression coverage for placeholder skipping, publish-tree assembly, and shared resource setup.